A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
When a projection system is used to transfer the pattern onto the substrate, any aberrations in the projection system will affect the projected image and should be minimized. A perfect projection system cannot be made so most projection systems are provided with adjustment “knobs” which control the position and/or orientation of one or more optical elements in the projections system, e.g. lens or mirrors. Adjustment of these knobs affects the projected image, either by increasing or reducing aberrations. When the apparatus is set up, and when maintenance is required, wavefront aberrations in the projected image are measured and the knobs of the projection system adjusted to minimize these.
This is not a straight forward procedure: it requires a mathematical model or simulation of the projection system to link the measured wavefront errors to the available control knobs. It is convenient to describe aberrations and wavefront errors in terms of Zernike polynomials and these are generally used for the input to the model of the projection system. However, determination of the values of individual Zernike polynomials is not always possible as it generally requires an interferometer built into the apparatus, which is not always available. Also, some measurement techniques have difficulty in distinguishing between aberrations of the same type, but different order.